Finite Group Databasebeta

← C47×#24044 #26063742

Subgroups — C47×#24044 #26063742

Order 12032.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C47C211yesmaximal, characteristic
2C2×C47×#482C211yesmaximal, characteristic, complemented
3C2×C47×#418C211yesmaximal, characteristic, complemented
4C47×#2485C211yesmaximal, characteristic, complemented
5C47×#2041C211yesmaximal, characteristic, complemented
6C47×#2041C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#1895C211yesmaximal, characteristic, complemented
10C47×#1870C211yesmaximal, characteristic, complemented
11C47×#1864C211yesmaximal, characteristic, complemented
12C47×#1862C211yesmaximal, characteristic, complemented
13C47×#1786C211yesmaximal, characteristic, complemented
14C47×#1786C211yesmaximal, characteristic, complemented
15C47×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C47—21no—
17C23×D4×C47C2211yescharacteristic
18C23×D4×C47C2211yescharacteristic
19C22×M16×C47C2211yescharacteristic, complemented
20D42×C47—24no—
21D42×C47—24no—
22C2×#127×C47C2211yescharacteristic
23C2×#121×C47—21no—
24C2×#121×C47C2211yescharacteristic
25C2×#121×C47C2211yescharacteristic
26C2×#120×C47—21no—
27C2×#120×C47—21no—
28C2×C4×D4×C47C2211yescharacteristic
29C2×C4×D4×C47C2211yescharacteristic
30C2×#117×C47C2211yescharacteristic, complemented
31C47×#482—24no—
32C2×#107×C47C2211yescharacteristic, complemented
33C2×#106×C47C2211yescharacteristic, complemented
34C47×#418—24no—
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×#102×C47C2211yescharacteristic
39C2×#102×C47C2211yescharacteristic, complemented
40C2×#102×C47C2211yescharacteristic, complemented
41C2×#102×C47C2211yescharacteristic, complemented
42C2×#102×C47C2211yescharacteristic, complemented
43C2×#102×C47C2211yescharacteristic, complemented
44C2×#102×C47C2211yescharacteristic, complemented
45C2×#102×C47C2211yescharacteristic, complemented
46C2×#102×C47C2211yescharacteristic, complemented
47C2×C22⋊C8×C47C2211yescharacteristic, complemented
48C2×C22⋊C8×C47C2211yescharacteristic, complemented
49C2×C22⋊C8×C47C2211yescharacteristic, complemented
50C47×#397—21no—
51C47×#394—21no—
52C47×#389C2211yescharacteristic, complemented
53C47×#389C2211yescharacteristic, complemented
54C47×#388—21no—
55C47×#387—21no—
56C47×#380C2211yescharacteristic, complemented
57C47×#380C2211yescharacteristic, complemented
58C47×#380C2211yescharacteristic, complemented
59C47×#340C2211yescharacteristic, complemented
60C47×#340C2211yescharacteristic, complemented
61C47×#336C2211yescharacteristic, complemented
62C47×#336C2211yescharacteristic, complemented
63C25×C47—21no—
64C25×C47—21no—
65C22×D4×C47—22no—
66C22×D4×C47—22no—
67C22×D4×C47—28no—
68C22×D4×C47—21no—
69C22×D4×C47—21no—
70C22×D4×C47—22no—
71C22×D4×C47—22no—
72C22×D4×C47—22no—
73C22×D4×C47—22no—
74C22×D4×C47—21no—
75C22×D4×C47—21no—
76C22×D4×C47—21no—
77C22×D4×C47—22no—
78C22×D4×C47—21no—
79C22×D4×C47—41no—
80C22×D4×C47—41no—
81C22×D4×C47—41no—
82C22×D4×C47—41no—
83C22×D4×C47—44no—
84C22×D4×C47—44no—
85C22×D4×C47D411yescharacteristic
86C22×D4×C47D414yes—
87C22×D4×C47C2311yescharacteristic
88C22×D4×C47C2311yescharacteristic
89C22×D4×C47C2311yescharacteristic
90C23×C4×C47—21no—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C2×M16×C47—22no—
94C2×M16×C47—41no—
95C2×M16×C47—41no—
96C22×C8×C47C2311yescharacteristic
97C22×C8×C47C2311yescharacteristic
98C22×C8×C47C2311yescharacteristic
99C22×C8×C47C2311yescharacteristic
100#127×C47—22no—
101#127×C47—22no—
102#121×C47—28no—
103#121×C47—22no—
104#121×C47—22no—
105#121×C47—22no—
106#121×C47D414yes—
107#120×C47—28no—
108#120×C47—28no—
109C4×D4×C47—22no—
110C4×D4×C47—22no—
111C4×D4×C47—22no—
112C4×D4×C47—22no—
113#117×C47—22no—
114#117×C47—22no—
115C2×C4⋊C4×C47—21no—
116C2×C4⋊C4×C47—21no—
117C2×C4⋊C4×C47D411yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C4⋊C4×C47C2311yescharacteristic
120C2×C4⋊C4×C47C2311yescharacteristic
121C2×C4⋊C4×C47C2311yescharacteristic
122C2×C4⋊C4×C47C2311yescharacteristic
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—21no—
125C2×C22⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C42×C47—21no—
133C2×C42×C47C2311yescharacteristic
134#107×C47—22no—
135#106×C47—22no—
136#102×C47—22no—
137#102×C47—22no—
138#102×C47—22no—
139#102×C47—22no—
140#102×C47—22no—
141#102×C47—22no—
142#102×C47—22no—
143#102×C47—22no—
144#102×C47—41no—
145#102×C47—41no—
146#102×C47—41no—
147#102×C47—41no—
148C22⋊C8×C47—22no—
149C22⋊C8×C47—41no—
150C22⋊C8×C47—41no—
151#95×C47—21no—
152#95×C47—21no—
153#95×C47—21no—
154#95×C47—21no—
155#95×C47—21no—
156C24×C47—21no—
157C24×C47—24no—
158C24×C47—21no—
159C24×C47—21no—
160C24×C47—24no—
161C24×C47—42no—
162C24×C47—42no—
163C24×C47—42no—
164C24×C47—42no—
165C24×C47—42no—
166C24×C47—42no—
167C24×C47—42no—
168C24×C47—42no—
169C24×C47—81no—
170C24×C47—81no—
171C24×C47—81no—
172C24×C47—81no—
173C24×C47C2×D411yescharacteristic
174C24×C47C2×D411yescharacteristic
175C2×D4×C47—22no—
176C2×D4×C47—22no—
177C2×D4×C47—28no—
178C2×D4×C47—24no—
179C2×D4×C47—24no—
180C2×D4×C47—24no—
181C2×D4×C47—24no—
182C2×D4×C47—24no—
183C2×D4×C47—24no—
184C2×D4×C47—22no—
185C2×D4×C47—21no—
186C2×D4×C47—21no—
187C2×D4×C47—21no—
188C2×D4×C47—21no—
189C2×D4×C47—21no—
190C2×D4×C47—21no—
191C2×D4×C47—21no—
192C2×D4×C47—21no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—44no—
199C2×D4×C47—44no—
200C2×D4×C47—44no—
201C2×D4×C47—42no—
202C2×D4×C47—42no—
203C2×D4×C47—42no—
204C2×D4×C47—42no—
205C2×D4×C47—42no—
206C2×D4×C47—44no—
207C2×D4×C47—44no—
208C2×D4×C47—432no—
209C2×D4×C47—44no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47—44no—
215C2×D4×C47—42no—
216C2×D4×C47—81no—
217C2×D4×C47—81no—
218C2×D4×C47C2×D412yes—
219C2×D4×C47C2×D412yes—
220C2×D4×C47C2×D412yes—
221C2×D4×C47#4112yes—
222C2×D4×C47#4112yes—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—24no—
228C22×C4×C47—21no—
229C22×C4×C47—21no—
230C22×C4×C47—21no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47—21no—
235C22×C4×C47—21no—
236C22×C4×C47—21no—
237C22×C4×C47—21no—
238C22×C4×C47—21no—
239C22×C4×C47—42no—
240C22×C4×C47—42no—
241C22×C4×C47C2×D411yescharacteristic
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47C2×D411yescharacteristic
244C22×C4×C47C2×D412yes—
245C22×C4×C47C2×D412yes—
246C22×C4×C47C2×D411yescharacteristic
247C22×C4×C47C2411yescharacteristic
248M16×C47—44no—
249C2×C8×C47—21no—
250C2×C8×C47—21no—
251C2×C8×C47—21no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C4⋊C4×C47—22no—
262C4⋊C4×C47—21no—
263C4⋊C4×C47—21no—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—21no—
271C4⋊C4×C47—42no—
272C4⋊C4×C47—81no—
273C4⋊C4×C47C2×D412yes—
274C22⋊C4×C47—24no—
275C22⋊C4×C47—24no—
276C22⋊C4×C47—22no—
277C22⋊C4×C47—24no—
278C22⋊C4×C47—22no—
279C22⋊C4×C47—42no—
280C22⋊C4×C47—42no—
281C22⋊C4×C47—81no—
282C22⋊C4×C47—81no—
283C42×C47—21no—
284C42×C47—21no—
285C42×C47—42no—
286C23×C47—21no—
287C23×C47—22no—
288C23×C47—21no—
289C23×C47—21no—
290C23×C47—21no—
291C23×C47—21no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—21no—
301C23×C47—22no—
302C23×C47—22no—
303C23×C47—48no—
304C23×C47—48no—
305C23×C47—48no—
306C23×C47—48no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47—41no—
321C23×C47—41no—
322C23×C47—41no—
323C23×C47—84no—
324C23×C47—84no—
325C23×C47—84no—
326C23×C47—84no—
327C23×C47—84no—
328C23×C47—84no—
329C23×C47—84no—
330C23×C47—84no—
331C23×C47—84no—
332C23×C47—84no—
333C23×C47#12012yes—
334C23×C47AGL(1,ℤ/8)12yes—
335C23×C47C22×D411yescharacteristic
336D4×C47—28no—
337D4×C47—22no—
338D4×C47—22no—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—22no—
343D4×C47—22no—
344D4×C47—48no—
345D4×C47—48no—
346D4×C47—48no—
347D4×C47—48no—
348D4×C47—48no—
349D4×C47—41no—
350D4×C47—41no—
351D4×C47—41no—
352D4×C47—41no—
353D4×C47—84no—
354D4×C47#12314yes—
355C2×C4×C47—21no—
356C2×C4×C47—21no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—22no—
362C2×C4×C47—22no—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—22no—
366C2×C4×C47—21no—
367C2×C4×C47—21no—
368C2×C4×C47—21no—
369C2×C4×C47—21no—
370C2×C4×C47—48no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—41no—
383C2×C4×C47—41no—
384C2×C4×C47—41no—
385C2×C4×C47—41no—
386C2×C4×C47—41no—
387C2×C4×C47—41no—
388C2×C4×C47—41no—
389C2×C4×C47#12012yes—
390C2×C4×C47AGL(1,ℤ/8)12yes—
391C2×C4×C47C22×D411yescharacteristic
392C2×C4×C47C22×D411yescharacteristic
393C2×C4×C47C2×#4111yescharacteristic
394C2×C4×C47C2×#4111yescharacteristic
395C2×C4×C47H(5,𝔽2)11yescharacteristic
396C2×C4×C47H(5,𝔽2)11yescharacteristic
397C8×C47—41no—
398C8×C47—41no—
399C8×C47—41no—
400C8×C47—41no—
401#24044C4711yesmaximal, characteristic, direct product factor, Sylow
402C22×C47—22no—
403C22×C47—24no—
404C22×C47—22no—
405C22×C47—22no—
406C22×C47—22no—
407C22×C47—22no—
408C22×C47—22no—
409C22×C47—41no—
410C22×C47—42no—
411C22×C47—41no—
412C22×C47—42no—
413C22×C47—41no—
414C22×C47—42no—
415C22×C47—41no—
416C22×C47—42no—
417C22×C47—41no—
418C22×C47—41no—
419C22×C47—42no—
420C22×C47—41no—
421C22×C47—41no—
422C22×C47—42no—
423C22×C47—42no—
424C22×C47—42no—
425C22×C47—42no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—816no—
430C22×C47—816no—
431C22×C47—81no—
432C22×C47—81no—
433C22×C47—81no—
434C22×C47—81no—
435C22×C47—81no—
436C22×C47—81no—
437C22×C47—81no—
438C22×C47—81no—
439C22×C47C2×#12011yescharacteristic
440C22×C47#54611yescharacteristic
441C22×C47#54611yescharacteristic
442C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
444C22×C47#57611yescharacteristic
445C22×C47#57711yescharacteristic
446C4×C47—22no—
447C4×C47—22no—
448C4×C47—41no—
449C4×C47—42no—
450C4×C47—41no—
451C4×C47—81no—
452C4×C47—81no—
453C4×C47—81no—
454C4×C47—81no—
455C4×C47C2×#12311yescharacteristic
456C4×C47#53411yescharacteristic
457C4×C47#54611yescharacteristic
458C4×C47#54611yescharacteristic
459C2×D42C2×C4711yescharacteristic
460C2×#482C2×C4711yescharacteristic, complemented
461C2×#418C2×C4711yescharacteristic, complemented
462#2485C2×C4711yescharacteristic, complemented
463#2041C2×C4711yescharacteristic, complemented
464#2041C2×C4711yescharacteristic, complemented
465#2034C2×C4711yescharacteristic, complemented
466#2033C2×C4711yescharacteristic, complemented
467#1895C2×C4711yescharacteristic, complemented
468#1870C2×C4711yescharacteristic, complemented
469#1864C2×C4711yescharacteristic, complemented
470#1862C2×C4711yescharacteristic, complemented
471#1786C2×C4711yescharacteristic, complemented
472#1786C2×C4711yescharacteristic, complemented
473#1786C2×C4711yescharacteristic, complemented
474C2×C47—42no—
475C2×C47—42no—
476C2×C47—44no—
477C2×C47—82no—
478C2×C47—82no—
479C2×C47#240511yescharacteristic
480C2×C47#300311yescharacteristic
481C2×C47#301211yescharacteristic
482C2×C47#331011yescharacteristic
483C2×C47#331811yescharacteristic
484C2×C47#332411yescharacteristic
485C2×C47#332511yescharacteristic
486C23×D4—21no—
487C23×D4C22×C4711yescharacteristic
488C23×D4C22×C4711yescharacteristic
489C22×M16C22×C4711yescharacteristic, complemented
490D42—24no—
491D42—24no—
492C2×#127C22×C4711yescharacteristic
493C2×#121—21no—
494C2×#121C22×C4711yescharacteristic
495C2×#121C22×C4711yescharacteristic
496C2×#120—21no—
497C2×#120—21no—
498C2×C4×D4C22×C4711yescharacteristic
499C2×C4×D4C22×C4711yescharacteristic
500C2×#117C22×C4711yescharacteristic, complemented
501#482—24no—
502C2×#107C22×C4711yescharacteristic, complemented
503C2×#106C22×C4711yescharacteristic, complemented
504#418—24no—
505C2×#102C22×C4711yescharacteristic
506C2×#102C22×C4711yescharacteristic
507C2×#102C22×C4711yescharacteristic
508C2×#102C22×C4711yescharacteristic
509C2×#102C22×C4711yescharacteristic, complemented
510C2×#102C22×C4711yescharacteristic, complemented
511C2×#102C22×C4711yescharacteristic, complemented
512C2×#102C22×C4711yescharacteristic, complemented
513C2×#102C22×C4711yescharacteristic, complemented
514C2×#102C22×C4711yescharacteristic, complemented
515C2×#102C22×C4711yescharacteristic, complemented
516C2×#102C22×C4711yescharacteristic, complemented
517C2×C22⋊C8C22×C4711yescharacteristic, complemented
518C2×C22⋊C8C22×C4711yescharacteristic, complemented
519C2×C22⋊C8C22×C4711yescharacteristic, complemented
520#397—21no—
521#394—21no—
522#389C22×C4711yescharacteristic, complemented
523#389C22×C4711yescharacteristic, complemented
524#388—21no—
525#387—21no—
526#380C22×C4711yescharacteristic, complemented
527#380C22×C4711yescharacteristic, complemented
528#380C22×C4711yescharacteristic, complemented
529#340C22×C4711yescharacteristic, complemented
530#340C22×C4711yescharacteristic, complemented
531#336C22×C4711yescharacteristic, complemented
532#336C22×C4711yescharacteristic, complemented
533C47#2404411yescharacteristic, direct product factor, Sylow
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C4711yescharacteristic
557C22×D4D4×C4714yes—
558C22×D4C23×C4711yescharacteristic
559C22×D4C23×C4711yescharacteristic
560C22×D4C23×C4711yescharacteristic
561C23×C4—21no—
562C23×C4C23×C4711yescharacteristic
563C23×C4C23×C4711yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C4711yescharacteristic
568C22×C8C23×C4711yescharacteristic
569C22×C8C23×C4711yescharacteristic
570C22×C8C23×C4711yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C4714yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C4711yescharacteristic
589C2×C4⋊C4C23×C4711yescharacteristic
590C2×C4⋊C4C23×C4711yescharacteristic
591C2×C4⋊C4C23×C4711yescharacteristic
592C2×C4⋊C4C23×C4711yescharacteristic
593C2×C4⋊C4C23×C4711yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C4711yescharacteristic
602C2×C22⋊C4D4×C4711yescharacteristic
603C2×C42—21no—
604C2×C42C23×C4711yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C4711yescharacteristic
645C24C2×D4×C4711yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C4712yes—
690C2×D4C2×D4×C4712yes—
691C2×D4C2×D4×C4712yes—
692C2×D4#41×C4712yes—
693C2×D4#41×C4712yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C4711yescharacteristic
713C22×C4C2×D4×C4711yescharacteristic
714C22×C4C2×D4×C4711yescharacteristic
715C22×C4C2×D4×C4712yes—
716C22×C4C2×D4×C4712yes—
717C22×C4C2×D4×C4711yescharacteristic
718C22×C4C24×C4711yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C4712yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C4712yes—
805C23AGL(1,ℤ/8)×C4712yes—
806C23C22×D4×C4711yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C4714yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C4712yes—
861C2×C4AGL(1,ℤ/8)×C4712yes—
862C2×C4C22×D4×C4711yescharacteristic
863C2×C4C22×D4×C4711yescharacteristic
864C2×C4C2×#41×C4711yescharacteristic
865C2×C4C2×#41×C4711yescharacteristic
866C2×C4H(5,𝔽2)×C4711yescharacteristic
867C2×C4H(5,𝔽2)×C4711yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—24no—
876C22—22no—
877C22—22no—
878C22—22no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—42no—
883C22—41no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—42no—
891C22—41no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C4711yescharacteristic
910C22C47×#54611yescharacteristic
911C22C47×#54611yescharacteristic
912C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
913C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
914C22C47×#57611yescharacteristic
915C22C47×#57711yescharacteristic
916C4—22no—
917C4—22no—
918C4—41no—
919C4—42no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C4711yescharacteristic
926C4C47×#53411yescharacteristic
927C4C47×#54611yescharacteristic
928C4C47×#54611yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C47×#240511yescharacteristic
935C2C47×#300311yescharacteristic
936C2C47×#301211yescharacteristic
937C2C47×#331011yescharacteristic
938C2C47×#331811yescharacteristic
939C2C47×#332411yescharacteristic
940C2C47×#332511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC2×D42×C47C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C47×#482C2semidirect
3. C2×C47×#418C2semidirect
4. C47×#2485C2semidirect
5. C47×#2041C2semidirect
6. C47×#2041C2semidirect
7. C47×#2034C2semidirect
8. C47×#2033C2semidirect
9. C47×#1895C2semidirect
10. C47×#1870C2semidirect
11. C47×#1864C2semidirect
12. C47×#1862C2semidirect
13. C47×#1786C2semidirect
14. C47×#1786C2semidirect
15. C47×#1786C2semidirect
19. C22×M16×C47C22semidirect
30. C2×#117×C47C22semidirect
32. C2×#107×C47C22semidirect
33. C2×#106×C47C22semidirect
39. C2×#102×C47C22semidirect
40. C2×#102×C47C22semidirect
41. C2×#102×C47C22semidirect
42. C2×#102×C47C22semidirect
43. C2×#102×C47C22semidirect
44. C2×#102×C47C22semidirect
45. C2×#102×C47C22semidirect
46. C2×#102×C47C22semidirect
47. C2×C22⋊C8×C47C22semidirect
48. C2×C22⋊C8×C47C22semidirect
49. C2×C22⋊C8×C47C22semidirect
52. C47×#389C22semidirect
53. C47×#389C22semidirect
56. C47×#380C22semidirect
57. C47×#380C22semidirect
58. C47×#380C22semidirect
59. C47×#340C22semidirect
60. C47×#340C22semidirect
61. C47×#336C22semidirect
62. C47×#336C22semidirect
401. #24044C47direct (N × H)
460. C2×#482C2×C47semidirect
461. C2×#418C2×C47semidirect
462. #2485C2×C47semidirect
463. #2041C2×C47semidirect
464. #2041C2×C47semidirect
465. #2034C2×C47semidirect
466. #2033C2×C47semidirect
467. #1895C2×C47semidirect
468. #1870C2×C47semidirect
469. #1864C2×C47semidirect
470. #1862C2×C47semidirect
471. #1786C2×C47semidirect
472. #1786C2×C47semidirect
473. #1786C2×C47semidirect
489. C22×M16C22×C47semidirect
500. C2×#117C22×C47semidirect
502. C2×#107C22×C47semidirect
503. C2×#106C22×C47semidirect
509. C2×#102C22×C47semidirect
510. C2×#102C22×C47semidirect
511. C2×#102C22×C47semidirect
512. C2×#102C22×C47semidirect
513. C2×#102C22×C47semidirect
514. C2×#102C22×C47semidirect
515. C2×#102C22×C47semidirect
516. C2×#102C22×C47semidirect
517. C2×C22⋊C8C22×C47semidirect
518. C2×C22⋊C8C22×C47semidirect
519. C2×C22⋊C8C22×C47semidirect
522. #389C22×C47semidirect
523. #389C22×C47semidirect
526. #380C22×C47semidirect
527. #380C22×C47semidirect
528. #380C22×C47semidirect
529. #340C22×C47semidirect
530. #340C22×C47semidirect
531. #336C22×C47semidirect
532. #336C22×C47semidirect
533. C47#24044direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×D42×C472
C2×C47×#4822
C2×C47×#4182
C47×#24852
C47×#20412
C47×#20342
C47×#20332
C47×#18952
C47×#18702
C47×#18642
C47×#18622
C47×#17862
#2404447